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    $\begingroup$ A quick comment, in lieu of a possibly better answer, etc: in my opinion, you are quite correct in perceiving/feeling/thinking that it would be extremely difficult (impossible, really) to "prove everything for yourself" in this field. For that matter, all my experience indicates that it is equally ridiculous to imagine that novices would be able to prove for themselves all the major results in any field at all. Whoa, yes, the problem is an over-interpretation of Moore-method ideas: sure, it's good to think about thing oneself... but [cont'd] $\endgroup$ Commented Feb 14, 2019 at 23:32
  • 13
    $\begingroup$ ... [cont'd] we should admit that many other very smart, hard-working people have come up with many great ideas, which we'd only eventually experimentally discover after centuries of trial-and-error, if then. Sure, let's not discourage ourselves by thinking that the big-shots of the past did everything... but we should respect not only the historically-notable, but also many other, people just as smart/talented as we are who worked hard their whole lives to understand things. $\endgroup$ Commented Feb 14, 2019 at 23:33
  • 15
    $\begingroup$ In complementary to what @paulgarrett said, I think you should interpret that sentence ("attempting to prove it by myself") as stressed on the word "attempting". It's impossible (and pointless) to prove everything by yourself, but "attempting" to do so will give you a much better idea of where the difficulty of the problem lies, hence a deeper understanding when you read the proof. $\endgroup$ Commented Feb 14, 2019 at 23:38
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    $\begingroup$ As @WhatsUp commented, indeed, "attempting and failing" is almost universally hugely informative (not to mention modesty/humility-generating). A relatively minor issue is about how much time to allocate to a probably-failing venture before declaring it operationally hopeless. A non-trivial question. $\endgroup$ Commented Feb 15, 2019 at 0:03
  • 15
    $\begingroup$ I think that the "overarching idea behind the study of analytic number theory" is that analytic methods are highly effective in answering questions about numbers. If you like analysis and numbers, then it is for you, otherwise it is not. BTW Langlands famously said that "analytic number theory lacks concepts". Well, I don't know. I think $L$-function is a great concept. $\endgroup$ Commented Feb 15, 2019 at 2:36